Science Testing Document

Input

static_leakage_matrix has 3 inputs at command line. One integer L such that the static part of the leakage matrix is computed for target modes in the degree range [0,L]. One integer d such that leaks are computed only for modes in l-range [L-d,L+d] and m-range [m-d,m+d] and the name of a fits file where to write into the static-leakage-matrix coefficients. Example of inputs : 15 3 /users/Mike/static_leakage_matrix.fits.

leakage_matrix has 4 inputs at command line. 2 integers L and d as previously described, the name of a fits file containing static-leakage-matrix coefficients as output by static_leakage_matrix and the name of a fits file where to write into the leakage matrix elements. Example of a fits file of static-leakage-matrix coefficients for L=50 and d=10: static_leakage_50_10.fits.

optimal_sph_coeff has 9 inputs at command line: 3 integers l,m and n which are target mode- degree, azimuthal order and order, respectively, and L and d as previously described. 3 filenames for 3 files which will contain the filtered time series for the target, the target mode profile and the parameters, respectivelyopt_sph_coeff requests also as inputs :

a fits file containing leakage-matrix coefficients as output by leakage_matrix. Example of a fits file of leakage-matrix coefficients for L=50 and d=10: leakage_matrix_50_10.fits

a table of mode frequencies (currently MDI frequencies). The filename and the size of the table are given in the define section of the code:

Only L_MAX, DELTA_LM, PRINT_RESULTS and TEST_SUITE might be changed by the user.
Leakage matrix coefficients are then accordingly computed for target modes of degree l in the range 0-L_MAX and azimuthal order |m|<=l
and for leak-modes of degree l' and aimuthal order m' satisfying |l-l'|<=DELTA_LM and |m-m'|<=DELTA_LM.
If PRINT_RESULTS is set to

true

the coefficients are printed out on the standard output.
Set TEST_SUITE to

true

when compiling with CuTest for test purpose.
PSF_WIDTH, R_IN and R_OUT shall be fixed once given by HMI team. The constant T_LIM shall be fixed accordingly.
The current numbers are those of MDI.
N_GRID1 and N_GRID2 if changed affect the precision of the output and the computation time.

optimal_sph_coeff includes in addition another file of constants (optimal_constants.h).

Expected Output

final output:

output for static_leakage_matrix is a fits file containing the static leakage matrix coefficients as an array of size (L+1).(L+1)x(2d+1)x(2d+1). Example of such a fits file for L=50 and d=10: static_leakage_50_10.fits. /overwrite allows to overwrite the output file if it already exists.

limitations of algorithm: Currently the algorithm is li,ited to degrees up to l=10

Unit Testing

Classes with unit tests:

leakage_matrix.c (contains currently 105 tests).

optimal_sph_coeff.c (contains currently 76 tests).

static_leakage_matrix.c (contains currently 48 tests).

Science Test Cases

Case 1: Optimal time series for a target

a. Target l=1 m=1 n=20

Description

The aim of this science test is to produce a time series of 2 years with a sampling of 60sec. which is optimal for a given target mode.
Optimal means that modes adjacent (leak-modes) to the target are filtered out in a frequency window of +/- FRE_WIN as provided into the optimal_constant.h header file.
The target mode is a low-degree mode l=1, m=1, n=20 located around 2963 uHz.
The timeseries is produced using existing MDI (SHT) time series. The timeseries are combined using weights coefficients provided by optimal_sph_coeff

Output

The output is the file l1_m1_n20_timeseries.fits
containing a string of data which is a timeseries of 2 years with a sampling of 60sec and optimized for the target .

b. Target l=10 m=0 n=15

Description

The aim of this science test is to produce a time series of 2 years with a sampling of 60sec. which is optimal for a given target mode.
Optimal means that modes adjacent (leak-modes) to the target are filtered out in a frequency window of +/- FRE_WIN as provided into the optimal_constant.h header file.
The target mode is a low-degree mode l=10, m=0, n=15 located around 2716 uHz.
The timeseries is produced using existing MDI (SHT) time series. The timeseries are combined using weights coefficients provided by optimal_sph_coeff

Output

The output is the file l10_m0_n15_timeseries.fits
containing a string of data which is a timeseries of 2 years with a sampling of 60sec and optimized for the target .

Case 2: Optimal power spectrum for a target

a. Target l=1 m=1 n=20

Description

The aim of this science test is to produce a power spectrum which is optimal for the given target mode.
Optimal means that modes adjacent (leak-modes) to the target are filtered out in a frequency window of +/- FRE_WIN as provided into the optimal_constant.h header file.
The target mode is the low-degree mode l=1, m=1, n=20 located around 2963 uHz.
The power spectrum is produced using the optimal timeseries of the Case 1.

Input

Output

The output is a file containing the profile of the target in the power spectrum l1_m1_n20_profile.dat.
It contains 2 columns : the left one is for the frequency and the right is the mode power.

b. Target l=10 m=0 n=15

Description

The aim of this science test is to produce a power spectrum which is optimal for the given target mode.
Optimal means that modes adjacent (leak-modes) to the target are filtered out in a frequency window of +/- FRE_WIN as provided into the optimal_constant.h header file.
The target mode is the low-degree mode l=10, m=0, n=15 located around 2716uHz.
The power spectrum is produced using the optimal timeseries of the Case 1.

Input

Output

The output is a file containing the profile of the target in the power spectrum l10_m0_n15_profile.dat.
It contains 2 columns : the left one is for the frequency and the right is the mode power.

Case 3: Mode parameters for a target

Target l=1 m=1 n=20

Description

The aim of this science case is to extract the parameters of the target mode : its frequency, amplitude, linewidth
and background nioise by fitting the mode profile l1_m1_n20_profile.dat
with a method of likelihood maximization. The current model is that of an asymmetrical Lorentzian profile.

Input

Expected Output

the output is file containing the mode parameters with the correspondings error bars l1_m1_n20_parameters.dat of optimal_sph_coeff
which prints out the results of the fitting.

Target l=10 m=0 n=15

Description

The aim of this science case is to extract the parameters of the target mode : its frequency, amplitude, linewidth
and background nioise by fitting the mode profile l10_m0_n15_profile.dat
with a method of likelihood maximization. The current model is that of a Lorentzian profile.